Create New Account
Create New Account

Sign in to Innings2

or

New Account     Reset Password     

Exponents and Powers

    Expressing Large Numbers in the Standard Form

Powered by Innings 2

Reset Progress

This will delete your progress and chat data for all chapters in this course, and cannot be undone!

Glossary

Select one of the keywords on the left…

7th class > Exponents and Powers > Expressing Large Numbers in the Standard Form

Expressing Large Numbers in the Standard Form

At the start of this chapter, we discussed how exponents are a convenient method for expressing large numbers. While we've touched on the concept, we haven't delved into specific examples or explanations. Let's address this now by exploring how exponents simplify the representation of large numbers.

  1. Sun is located 300,000,000,000,000,000,000 m from the centre of our Milky Way Galaxy.

  2. Number of stars in our Galaxy is 100,000,000,000.

  3. Mass of the Earth is 5,976,000,000,000,000,000,000,000 kg.

These numbers are not convenient to write and read.

To make it convenient we use powers.

Observe the following:

59=5.9×10=5.9×101
590=5.9×100=5.9×10
5900=5.9×1000=5.9× 10
59000=5.9×10000=5.9× 10 and so on.

We have expressed all these numbers in the standard form. Any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 multiplied by a power of 10. Such a form of a number is called its standard form.

Thus, 5,985=5.985×1000=5.985×103 is the form of 5,985.

Why? As the first part of the number (59.85) is not between 1 and 10, which is a requirement for standard scientific notation.

Note: 5,985 can also be expressed as 59.85 × 100 or 59.85 × 102

But these are not the standard forms, of 5,985. Similarly, 5,985=0.5985×10,0=0.5985×104 is also not the standard form of 5,985.

We are now ready to express the large numbers we came across at the beginning of the chapter in this form.

The, distance of Sun from the centre of our Galaxy i.e.,

300,000,000,000,000,000,000 m can be written as:

3.0 × 100,000,000,000,000,000,000 = 3.0 × 10 m

Mass of the Earth = 5,976,000,000,000,000,000,000,000 kg

= 5.976× 10 kg

Do you agree with the fact, that the number when written in the form is much easier to read, understand and compare than when the number is written with 25 digits?

Now, Mass of Uranus = 86,800,000,000,000,000,000,000,000 kg

=8.68× 10 kg

Simply by comparing the powers of 10 in the above two, you can tell that the mass of Uranus is greater than that of the Earth.

The distance between Sun and Saturn is 1,433,500,000,000 m or 1.4335×1012 m.

The distance betwen Saturn and Uranus is 1,439,000,000,000 m or 1.439×1012 m.

The distance between Sun and Earth is 149, 600,000,000 m or 1.496×1011 m.

Can you tell which of the three distances is smallest?

(i) 5985.3 =
5.9853 × 1000 = 5.9853 × 10^
Here, there are four digits to the left of the decimal point in 5985.3 and the exponent becomes 3 when converting to standard form.
(ii) 65,950 =
6.595 × 10,000 = 6.595 × 10^
In this case, there are five digits to the left of the decimal point in 65,950. and the exponent is 4.
(iii) 3,430,000 =
3.43 × 1,000,000 = 3.43 × 10^
For 3,430,000, there is no decimal point shown; we assume it to be at the (right) end. From there, the count of the places (digits) to the left is seven (digits to the left of the decimal point), and the exponent is 6.
(iv) 70,040,000,000=
7.004 × 10,000,000,000 = 7.004 x 10^
In 70,040,000,000, there are eleven digits to the left of the decimal point and the exponent is 10.

A point to remember is that one less than the digit count (number of digits) to the left of the decimal point in a given number is the exponent of 10 in the standard form.